Inequalities
Inequalities
Inequalities
Inequalities are mathematical sentences containing signs such as:
Sign

Meaning

Example

<

is less than

3 < 4

>

is greater than

4 > 3

≤

is less than or equal to

y ≤ 5

≥

is greater than or equal to

x ≥ 3

Inequations, or inequalities, can be solved in the same way as equations.
Example
2q + 3 > 4
2q > 1
q > 0.5
The only difference between equations and inequations is that when both sides of the inequation are
multiplied or divided by a negative number, the inequality sign must be reversed.
As with equations, some word problems can be solved by forming an inequality.
e.g. The sum of two numbers is less than 10 can be written mathematically as x + y < 10
Example
A man has $700 to spend on a suit and some shirts. He finds a new suit for $450 and the shirts cost $45 each. How many shirts can he buy?
Step 1 Form an inequality
Let the number of shirts the man can buy be x
45x + 450 ≤ 700
Step 2 Solve the inequality
45x + 450 ≤ 700
45x ≤ 700 − 450
45x ≤ 250
x ≤ 5.6 (to 2 s.f.)
Step 3 Write out the solution to the problem in words.
If x ≤ 5.6 then he can buy 5 shirts
When an inequality has been solved the solution can be shown on a number line.
e.g. Solve 3x + 6 < 21 for x is a member of R (x is a real number)
3x <15
x < 5